Download Chapter 29:Electromagnetic Induction and Faraday*s Law

Chapter 29:Electromagnetic
Induction and Faraday’s Law
28-4 Ampère’s Law
Example 28-8: A nice use for Ampère’s law.
Use Ampère’s law to show that in any region of
space where there are no currents the magnetic
field cannot be both unidirectional and nonuniform as shown in the figure.
Problem 27
27.
a
(I) A 2.5-mm-diameter copper wire carries
33-A
current
(uniform
across
its
cross
section). Determine the magnetic field: (a) at
the surface of the wire; (b) inside the wire,
0.50 mm below the surface; (c) outside the wire
2.5 mm from the surface.
28-4 Ampère’s Law
Solving problems using Ampère’s law:
• Ampère’s law is only useful for solving problems
when there is a great deal of symmetry.
Identify the symmetry.
• Choose an integration path that reflects the
symmetry (typically, the path is along lines
where the field is constant and perpendicular to
the field where it is changing).
• Use the symmetry to determine the direction
of the field.
• Determine the enclosed current.
28-5 Magnetic Field of a
Solenoid and a Toroid
A solenoid is a coil of wire containing many
loops. To find the field inside, we use Ampère’s
law along the path indicated in the figure.
28-5 Magnetic Field of a
Solenoid and a Toroid
The field is zero outside the solenoid, and the path
integral is zero along the vertical lines, so the field is (n
is the number of loops per unit length)
𝑩 = 𝝁𝟎 𝑛𝐼
N: number of Turns
l: length
28-5 Magnetic Field of a Solenoid and
a Toroid
Example 28-9: Field inside a solenoid.
A thin 10-cm-long solenoid used for fast
electromechanical switching has a total
of 400 turns of wire and carries a
current of 2.0 A. Calculate the field
inside near the center.
28-6 Biot-Savart Law
The Biot-Savart law gives the magnetic field
due to an infinitesimal length of current; the
total field can then be found by integrating over
the total length of all currents:
28-6 Biot-Savart Law
Example 28-11:BB due to current I in straight
wire.For the field near a long straight wire
carrying a current I, show that the Biot-Savart
law gives
B = μ0I/2πr.
Problem 37
37. (II) A wire is formed into the shape of two
half circles connected by equal-length straight
sections as shown in Fig. 28–45. A current I
flows in the circuit clockwise as shown. Determine
(a) the magnitude and direction of the magnetic
field at the center, C, and (b) the magnetic
dipole moment of the circuit.
29-1 Induced EMF
https://www.youtube.com/watch?v=gfJG4M4wi1o
29-1 Induced EMF
Almost 200 years ago, Faraday looked for evidence
that a change in a magnetic field would induce an
electric current with this apparatus:
29-1 Induced EMF
He found no evidence when the current was
steady, but did see a current induced when
the switch was turned on or off.